The pre-paid debit cards would tie into an unannounced service that would allow iPhone users to send money to each other digitally.

But some bank executives are reportedly wary, and plan to complain at a Visa "summit" next week, according to Recode's Jason Del Rey.

Apple has been rumored to be working on a peer-to-peer money transfer service or app since 2015. If launched, the service would be a direct competitor to PayPal's Venmo app.

A peer-to-peer service would matter to Apple because the company is looking to increase recurring revenue from selling services to its users.

Apple takes a slim cut, reportedly 0.15%, off purchases made with a credit card through its Apple Pay wallet service. But Apple Pay adoption has underwhelmed since it launched in 2014. Loup Ventures analyst Gene Munster estimates that Apple saw $36 billion in total Apple Pay transaction volume last year.